Question

Explain the relation between g and G

Answer 1

‘G' & ‘g' are related to gravitational force.

G is known as universal gravitational constant. Its numerical value is 6.67 × 10^-11 N-m²/Kg²

g is known as acceleration due to gravity. And its generally numerical value is 9.8 m/s². It is changeable. It is different for place in earth. g = 10 m/s² in Poles.

The relation between ‘G’ & ‘g' :-

According the Newton’s law of gravitation -

F = G M.m / r² -(I)

where M and m are two masses distance between r metre.

By Newton's second law :-

F = mg -(ii)

Where F is force and m is mass and g is acceleration due to gravity.

Now equating equation (i) and (ii) than:-

=mg = G M.m / r²

g = G M / r² -(iii)

The above eqn. (iii) is the relation between ‘G’ and ‘g'.